Emissive brightening in molecular graphene nanoribbons by twilight states

Carbon nanomaterials are expected to be bright and efficient emitters, but structural disorder, intermolecular interactions and the intrinsic presence of dark states suppress their photoluminescence. Here, we study synthetically-made graphene nanoribbons with atomically precise edges and which are designed to suppress intermolecular interactions to demonstrate strong photoluminescence in both solutions and thin films. The resulting high spectral resolution reveals strong vibron-electron coupling from the radial-breathing-like mode of the ribbons. In addition, their cove-edge structure produces inter-valley mixing, which brightens conventionally-dark states to generate hitherto-unrecognised twilight states as predicted by theory. The coupling of these states to the nanoribbon phonon modes affects absorption and emission differently, suggesting a complex interaction with both Herzberg–Teller and Franck– Condon coupling present. Detailed understanding of the fundamental electronic processes governing the optical response will help the tailored chemical design of nanocarbon optical devices, via gap tuning and side-chain functionalisation.


Supplementary Methods: Graphene nanoribbon sample preparation
Cove-edged graphene nanoribbons (GNRs) with dodecyl side chains (4-CGNR) (Supplementary Fig. 1) and cove-edged GNRs decorated with the Diels-Alder cycloadduct of anthracenyl unit and N-n-octadecylmaleimide (GNR-AOM) were prepared according to reported procedures [1-2].Ribbons have a length distribution of L=10-371 nm.AOM side chain as model was prepared following the reported similar synthetic route [3], 0.2 mg/ml GNR-AOM were dissolved in chloroform and briefly sonicated.For spectroscopic measurements at low temperatures, polystyrene (PS) or ethylene-vinyl acetate (EVA) polymer was added to the GNR solution in a 50:1 polymer to GNR ratio.The solution was consequently deposited on a glass substrate, which was heated to 50 o C, via drop casting to form a film of GNR in polymer matrix.We used two different transparent polymers, EVA and PS, to investigate possible effects of the polymer matrix.When comparing room temperature spectra of GNR in solution and in polymer matrix we found no effect of the polymer or solvent on PL, Raman or absorbance measurements at concentrations below 0.2 mg/ml in chloroform solution and 1:25 in transparent polymer matrix thin films, see Supplementary Fig. 9.

Supplementary Text 1: Fitting and Franck-Condon modelling the GNR optical response
To fit the optical response, we chose a staged process: First, we performed a free parameter fit on amplitude, width, and position in order to determine the energy of the transitions and hence the basic mechanism (top of Supplementary Fig. 7).For the PL, this requires eight Lorentzian peaks, one for the ZPL, five for the RBLM-mode, one for the G-mode, and one for low energy excimer emission.For the absorption, we chose nine Lorentzian peaks, one for the ZPL, three for the RBLM-mode, three for the G-mode, one for the E12 transition, and one for high energy absorption.
Fitting a single spectrum with this many parameters leaves room for uncertainty in the fitting result as this often leads to multiple solutions with similar accuracy.However, we found that when all parameters are free and independent, the results shown in Supplementary Fig. 7 were robustly reproducible under multiple varying starting parameters.This procedure shows us that the ZPL and 5 RBLM peaks form a single series of peaks with a very accurate spacing equal to the RBLM energy as shown in the inset Fig. 2d.
In the second step, we chose a fit function satisfying a simple Franck-Condon model which imposes conditions on the position, width and amplitude of the phonon peaks.
Franck-Condon modelling was performed according to previous studies [4].The intensity of a single FC progression coupled to a single phonon mode is calculated as with the intensity I, the photon energy ħω, the Huang-Rhys factor S, the 0-0 transition energy E0 (EZPL), phonon energy ħωi, and the line shape function Γ, which is assumed to be Lorentzian.For our material, the optical response can be modelled with the RBLM and G phonons as well as the zero-phonon line, see Supplementary Fig. 7.Note that the model does not include emission above or absorption below the ZPL energy which is thus excluded.In addition, the PL data contains a wide Lorentzian contribution from low energy emission due to defects and excimers.Similarly, the absorption has an additional wide Lorentzian contribution at higher energies and a narrow Lorentzian representing the second interband transition E12.Results of the modelling are given in Supplementary Table 2.
For the absorption spectrum, which is dominated by the G-mode, this works relatively well.However, the PL spectrum deviates from the predicted amplitude of a purely Franck-Condon model and we have thus included an extra peak for the 0-1 RBLM phonon to allow the fit function to match the data sufficiently well (Supplementary Fig. 7).Still, the fit function deviates from the data at energies approaching the G-mode peak around 1900meV.The higher RBLM modes at this point are significantly enhanced relative to the simple model which suggests the presence of a second phonon coupling mechanism such as Herzberg-Teller coupling, as discussed in the main text.

Supplementary Text 2: Zone folding of CNT(6,6) and cove-GNR
The electronic band structure of CNT(6,6) can be obtained by superimposing the graphene band structure at allowed k lines, which is the fundamental idea of zone-folding approximation.The first Brillouin zone of graphene is a hexagon, as shown in Supplementary Fig. 10.Assume the C-C bond length in graphene is , then the coordinates of rightmost K and K' are (2 3 ⁄ , 2 3√3 ⁄ ) and (2 3 ⁄ , − 2 3√3 ⁄ ) respectively.Suppose the CNT(6,6) and cove-GNR are both periodic along  direction.Since the nanotube is confined in the circumferential direction, its Brillouin zone is a vertical line of length 2 √3 ⁄ , as denoted by the green lines in Supplementary Fig. 10.Along the transverse direction there are only discrete allowed wavenumbers.For CNT(6,6) the horizontal k path F-M is divided into six parts.So we projected the band structure of CNT(6,6) on graphene band structure at these discrete k lines, from which we can see the contributions of graphene band structure to each band of CNT(6,6).For example, the highest unoccupied band and lowest occupied band of CNT(6,6) are contributed by the graphene band structure with transverse wavenumber   = 0.The lowest unoccupied band and highest occupied band are contributed by the graphene band structure with transverse wavenumber   = 2 3 ⁄ , i.e. the line passing through K and K' valleys.In contrast, the transverse wavenumber in cove-GNR is no longer a good quantum number, as the translational invariance in lateral direction is not well defined.Nonetheless we still choose the same k lines to project the band structure of cove-GNR in order to compare with that of CNT(6,6).One important difference of cove-GNR is that the unit cell along periodic direction is three times longer than that of the CNT(6,6).Therefore the first Brillouin zone of cove-GNR is one third of the first Brillouin zone of CNT(6,6).In Supplementary Fig. 11, the k lines are of the same length as Supplementary Fig. 10, but they correspond to three Brillouin zones of cove-GNR now.It can be directly seen from the diagram that both K and K' valleys are folded to Γ point in cove-GNR Brillouin zone.By looking at the projected band structure, we can conclude that the lowest unoccupied bands and highest occupied bands, which are the bands account for the optical transitions, are mainly contributed by the graphene band structure at k path passing through the K and K' points.And the two valleys are completely mixed at the Γ point in cove-GNR Brillouin zone.

Fig. 1 .
Chemical structure of dodecyl functionalised GNR (4-CGNR).Supplementary Fig. 6.D and G phonon mode positions of GNR-AOM resolved from the low temperature PL of GNR-AOM.a) High energy tail of the PL response of GNR-AOM excited with 2.33eV.At lower temperatures the D and G Raman modes can be resolved in the PL onset.b) Low temperature D and G mode positions retrieved via peak fitting.Both modes shift towards lower wavenumbers with increasing temperatures, confirming that phonon scattering rather than thermal expansion drive this shift [5].